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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 324 · 40 sums
TalentJR

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  2. 2.A square garden has an area of 2704 square m. How long is each side (in m)?
  3. 3.What is √3364? =
  4. 4.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  5. 5.A square garden has an area of 64 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 625 (b) 651 (c) 668
  7. 7.What is √5329? =
  8. 8.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is √225? =
  10. 10.Which of these is a perfect square? (a) 303 (b) 289 (c) 312
  11. 11.What is 73²? =
  12. 12.How many whole numbers lie between 30² and 31²?
  13. 13.Which of these is a perfect square? (a) 144 (b) 148 (c) 149
  14. 14.What is the smallest whole number by which 12 must be divided to get a perfect square?
  15. 15.What is 23²? =
  16. 16.How many whole numbers lie between 24² and 25²?
  17. 17.What is 66²? =
  18. 18.Which of these is a perfect square? (a) 487 (b) 484 (c) 501
  19. 19.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  20. 20.What is √361? =
  21. 21.A square garden has an area of 3600 square m. How long is each side (in m)?
  22. 22.What is the smallest whole number by which 24 must be divided to get a perfect square?
  23. 23.How many whole numbers lie between 16² and 17²?
  24. 24.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is 24²? =
  26. 26.What is √8836? =
  27. 27.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  28. 28.A square garden has an area of 1156 square m. How long is each side (in m)?
  29. 29.How many whole numbers lie between 46² and 47²?
  30. 30.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  32. 32.Which of these is a perfect square? (a) 410 (b) 400 (c) 432
  33. 33.What is √9025? =
  34. 34.Which of these is a perfect square? (a) 203 (b) 202 (c) 196
  35. 35.What is √729? =
  36. 36.How many whole numbers lie between 42² and 43²?
  37. 37.What is √9216? =
  38. 38.What is √2704? =
  39. 39.What is 18²? =
  40. 40.What is √529? =

Answer key

  1. 49
  2. 52
  3. 58
  4. 64
  5. 8
  6. 625
  7. 73
  8. 784
  9. 15
  10. 289
  11. 5329
  12. 60
  13. 144
  14. 3
  15. 529
  16. 48
  17. 4356
  18. 484
  19. 225
  20. 19
  21. 60
  22. 6
  23. 32
  24. 625
  25. 576
  26. 94
  27. 289
  28. 34
  29. 92
  30. 841
  31. 484
  32. 400
  33. 95
  34. 196
  35. 27
  36. 84
  37. 96
  38. 52
  39. 324
  40. 23

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